/*
Disconnected?
*/
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pil = pair<int, lint>;
using pli = pair<lint, int>;
const int MAX_N = 1e5 + 5;
const lint INF = 1e15;
int n, m;
int s, t;
int u, v;
vector<pil> adj[MAX_N];
bool seen[MAX_N];
lint min_dist[MAX_N];
void init() {
for (int i = 1; i <= n; i++) {
seen[i] = false;
min_dist[i] = INF;
}
}
priority_queue<pli, vector<pli>, greater<pli>> order;
vector<int> backtrack_adj[MAX_N];
void dijk(int start, bool do_backtrack) {
init();
min_dist[start] = 0;
order.push({0, start});
while (order.size()) {
int y = order.top().second;
order.pop();
if (seen[y]) continue;
seen[y] = true;
for (pil e : adj[y]) {
int z = e.first;
lint len = e.second;
lint new_dist = min_dist[y] + len;
if (new_dist < min_dist[z]) {
if (do_backtrack)
backtrack_adj[z] = {y};
min_dist[z] = new_dist;
order.push({new_dist, z});
} else if (new_dist == min_dist[z] && do_backtrack)
backtrack_adj[z].push_back(y);
}
}
}
bool seen2[MAX_N];
void dfs(int y) {
seen2[y] = true;
for (int z : backtrack_adj[y]) {
if (seen2[z]) continue;
dfs(z);
}
}
lint u_dist[MAX_N], v_dist[MAX_N];
lint v_dp[MAX_N];
bool v_seen[MAX_N];
lint find_v_dp(int y) {
if (v_seen[y]) return v_dp[y];
v_dp[y] = v_dist[y];
for (int z : backtrack_adj[y]) {
assert(seen2[z]);
v_dp[y] = min(v_dp[y], find_v_dp(z));
}
v_seen[y] = true;
return v_dp[y];
}
lint u_dp[MAX_N];
bool u_seen[MAX_N];
lint find_u_dp(int y) {
if (u_seen[y]) return u_dp[y];
u_dp[y] = u_dist[y];
for (int z : backtrack_adj[y]) {
assert(seen2[z]);
u_dp[y] = min(u_dp[y], find_u_dp(z));
}
u_seen[y] = true;
return u_dp[y];
}
int main() {
// freopen("commuter.in", "r", stdin);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int y, z;
lint len;
cin >> y >> z >> len;
adj[y].push_back({z, len});
adj[z].push_back({y, len});
}
dijk(s, true);
dfs(t);
for (int i = 1; i <= n; i++)
if (!seen2[i])
backtrack_adj[i].clear();
// cout << min_dist[t] << endl;
// for (int i = 1; i <= n; i++) {
// cout << i << ": ";
// for (int in : backtrack_adj[i])
// cout << in << " ";
// cout << endl;
// }
dijk(u, false);
for (int i = 1; i <= n; i++)
u_dist[i] = min_dist[i];
dijk(v, false);
for (int i = 1; i <= n; i++)
v_dist[i] = min_dist[i];
// for (int i = 1; i <= n; i++) {
// cout << i << ": " << u_dist[i] << " " << v_dist[i] << endl;
// }
lint ans = u_dist[v];
for (int w = 1; w <= n; w++) {
if (!seen2[w]) continue;
ans = min(ans, u_dist[w] + find_v_dp(w));
}
for (int w = 1; w <= n; w++) {
if (!seen2[w]) continue;
ans = min(ans, v_dist[w] + find_u_dp(w));
}
cout << ans << '\n';
}
